Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Submitted to the 46th IEEE CDC on 9 Mar 2007 Design of continuous-time flows on intertwined orbit spaces
 

Summary: Submitted to the 46th IEEE CDC on 9 Mar 2007
Design of continuous-time flows on intertwined orbit spaces
P.-A. Absil C. Lageman J. H. Manton
Abstract-- Consider a space M endowed with two or more
Lie group actions. Under a certain condition on the orbits of
the Lie group actions, we show how to construct a flow on
M that projects to prescribed flows on the orbit spaces of the
group actions. Hence, in order to design a flow that converges
to the intersection of given orbits, it suffices to design flows on
the various orbit spaces that display convergence to the desired
orbits, and then to lift these flows to M using the proposed
procedure. We illustrate the technique by creating a flow for
principal component analysis. The flow projects to a flow on the
Grassmann manifold that achieves principal subspace analysis
and to a flow on the "shape" manifold that converges to the
set of orthonormal matrices.
I. INTRODUCTION
Given a symmetric positive-definite n × n matrix A, we
say that a flow on the set Rn×p
of all the n × p real

  

Source: Absil, Pierre-Antoine - Département d'ingénierie Mathématique, Université Catholique de Louvain

 

Collections: Mathematics